1. Field of the Invention and the Related Art Statement
The present invention relates to a crystal resonator vibrating in a thickness-shear mode, and more particularly to a thickness shear crystal resonator having a large Q factor with smooth temperature characteristics. The present invention also relates to a method of manufacturing said thickness shear crystal resonator.
FIG. 1 shows an electric equivalent circuit of the thickness shear crystal resonator comprising a crystal plate and a pair of electrodes directly applied on opposite surfaces thereof The Q factor (figure of merit), which represents the efficiency of vibration of such a crystal resonator, is expressed by the following equation (1): ##EQU1## wherein, f represents a vibration frequency, C.sub.1 a capacitance of the crystal resonator, and R.sub.1 an impedance of the crystal resonator, which represents a resistance against the vibration of the crystal resonator. In order to make large the Q factor of the crystal resonator vibrating at a specified frequency, it is necessary to make the capacitance C.sub.1 and/or the impedance R.sub.1 of the crystal resonator small. The vibrating frequency f of the crystal resonator, for example, a thickness shear resonator made of AT cut quartz, is expressed by f.perspectiveto.1660.times.n/t, wherein the unit of the frequency f is KHz, n represents the order of vibration, which is equal to 1 for the fundamental wave and is equal to 3, 5 . . . for the 3rd, 5th . . . overtones, and t represents a thickness of the crystal plate whose unit is expressed by mm. Since the order of vibration is predetermined, the vibrating frequency f of the thickness shear crystal resonator depends on the thickness t of the crystal plate. Therefore, in order to decrease the capacitance C.sub.1 of the crystal resonator vibrating at the given frequency for obtaining the crystal resonator having a large Q factor, the size of the electrodes arranged on opposite surfaces of the crystal plate should be made small. However, there is a limitation in reducing the size of electrodes in the thickness shear crystal resonator due to the following reason.
FIG. 2 is a schematic view showing the general construction of a known thickness shear crystal resonator in which the electrodes are applied on the opposite surfaces of the crystal plate. In this crystal resonator, electrodes 2, 3 are provided on front and rear surfaces of a crystal plate 1 such that they are opposite to each other. The crystal plate 1 is held by supporting wires 4, 5 made of electrically conductive material and these wires are coupled with said electrodes 2, 3, respectively. These supporting wires 4, 5 are respectively connected to terminals 6, 7, which are fixed to a metal base 10a via insulators 8, 9. The base 10a is covered with a metal cover 10band the space formed by the base 10a and the cover 10b is filled with an inert gas. In general, the electrodes 2, 3 arranged on the opposite surfaces of the crystal plate 1 are formed by the vacuum evaporation. In the thickness shear crystal resonator, the crystal plate 1 vibrates or deviates in the direction parallel to the plane of the electrodes. When the crystal resonator vibrates in such thickness shear mode, a part of the crystal plate located between the opposite electrodes tends to deviate from each other by applying the electric power across the electrodes, but the remaining part of plate in the peripheral portion, on which electrodes are not arranged, works to resist against the deviation of the crystal part located between the electrodes. Therefore, in the crystal resonator having the crystal plate of a given dimension, if the size of electrodes is made small in order to decrease the capacitance C.sub.1 for obtaining the large Q factor, the impedance R.sub.1 will be naturally large, and it will be impossible to obtain the large Q factor. Thus, it is considered to make the electrodes as well as the peripheral portion of the crystal plate 1 on which the electrodes are not formed small as possible. However, in order to electrically isolate the electrode 2 formed on one surface of the crystal plate and the supporting wire 5 coupled therewith from the electrode 3 formed on the other surface of the crystal plate and the supporting wire 5 coupled therewith, the peripheral portion must have a certain width. Generally, the width of 1.about.2 mm is required for the peripheral portion of the crystal resonator. It is apparent from the above that there is a limitation to make the capacitance C.sub.1 of the crystal resonator small by reducing the size of electrodes.
On the other hand, the impedance R.sub.1 of the crystal resonator has a characteristic different from that of the resistance of general electric circuits. It represents a resistance against the mechanical vibration of the crystal plate. The causes for such resistance have not been solved completely yet, but the following four factors have been considered. The first factor is that the crystal located in the peripheral portion of the crystal resonator, on which the electrodes are not arranged, restricts the vibration of the crystal located in the central portion, on which the electrodes are provided, the second factor is that the supporting wires restrict the vibration, the third factor is that the phase of the vibration of the crystal located between the electrodes is deviated from the phase of the vibration reflected from the side edge of the crystal plate, and the fourth factor is that several kinds of defects generated in the crystal plate during the manufacturing process serve as the resistance. Under the situation mentioned above, various solutions have been suggested for making the impedance of the thickness shear crystal resonator small, hitherto. However, the fully satisfied solution has not been suggested yet, as explained in the following.
FIG. 4 shows a conventional crystal resonator, in which a crystal plate 1 is formed into a plano-convex, i.e. one surface of the crystal plate is formed as a convex surface and the other surface is formed as a plane surface, and the both surfaces are polished to become like a mirror surface. Such a plano-convex type crystal resonator is disclosed in U.S. Pat. No. 4,188,557. In such crystal resonator, it is possible to concentrate the vibrating energy into the center of the crystal resonator and the displacement of the peripheral portion becomes almost zero, so that the resistance caused by the first factor mentioned above can be reduced. And, since it is also possible to reduce the coupling of high-order contour signals, which is determined by the thickness and contour of the crystal plate, the resistance caused by the second factor can be decreased. Further, the both surfaces of the crystal plate are formed to become like a mirror surface, the resistance caused by the fourth factor can be also reduced. Therefore, the Q factor of this plano-convex type crystal resonator becomes high, but it has a serious drawback that the manufacturing process therefor is complex and thus the cost for manufacturing becomes high because at least one of the surface of the crystal plate should be ground into the convex shape. Therefore, the application of the plano-convex type crystal resonator is practically restricted to such an extent that the economical problem need not be discussed.
FIG. 5 shows another embodiment of the conventional crystal resonator, in which the impedance R.sub.1 is made small. In this embodiment, the peripheral edge of the crystal resonator 1 is beveled to form a tapered edge by lapping. Also in such a crystal resonator having the beveled edge, the displacement of vibration is concentrated in the central portion of the crystal plate and the loss due to the supporting wires at the edge of the crystal plate can be reduced. However, there is a limitation to make the impedance R.sub.1 small by conducting the beveling treatment to the peripheral edge of the crystal plate, and in case of the crystal resonator vibrating at a higher frequency, the beveling process becomes extremely difficult and further the effect of the beveling does not appear so remarkably. As stated above, the vibrating frequency f of the crystal resonator is predominantly determined by the thickness of the crystal plate 1. For example, the thickness of the crystal plate is 1.66 mm at the fundamental frequency of 1 MHz. And if the frequency is 10 MHz, the thickness becomes 0.166 mm. As apparent from this, as the vibrating frequency becomes higher, the thickness of the crystal plate becomes thinner. Thus, the beveling treatment could not be conducted to the crystal resonator having the frequency of about 10 MHz or more, generally.
Another method of making the impedance R.sub.1 small has been suggested in which the lapping treatment is conducted for forming the both surfaces of the crystal plate into the mirror surfaces. Generally, the crystal plate is lapped by means of abrasive grains after the plate being cut in the given orientation of the crystal. In the beginning of the lapping, coarse grains are used, and in the end, fine grains are used. The mesh size of grains for use in finishing is about #2500-#4000, whose diameter is about several microns. The grain size for use in finishing is determined by taking into consideration the necessary performance of the resonator in practical use and the cost therefor. If the crystal plate is lapped by using very fine abrasive grains without considering economical efficiency to obtain the mirror finished surface, the fourth factor will be reduced and the impedance R.sub.1 will become small to some extent. However, the cost therefor will be extremely expensive and not in practice. Furthermore, in the mechanical lapping using the grains, there is generated affected ground layers in the surfaces of the crystal plate, so that there is a limitation in making the impedance R.sub.1 small.
Furthermore, it is also suggested to conduct an etching treatment on the crystal plate in such manner that the whole crystal plate is immersed in an etching liquid, for example, a solution of ammonium fluoride, in order not only to reduce the impedance R.sub.1 but also to reduce the age variation of the vibration frequency by removing the affected ground layer generated in the surface of the crystal plate or by removing dirt or stain on the surface of the crystal plate. The impedance R.sub.1 can be made small by such etching treatment. However, if the surface of the crystal plate is over etched, the surface becomes rough, and the impedance R.sub.1 is increased. Further, not only the peripheral portion but also the central portion on which the electrodes are to be arranged are etched, so that the adhesive force of the electrodes to the surfaces of the crystal plate becomes weak. Moreover, a desired thickness of the crystal plate cannot be obtained, and the vibration frequency thereof might be shifted.
The thickness shear crystal resonators manufactured in a mass production scale are produced by such a way of cutting a crystal plate into a given shape, polishing the cut crystal plate by using abrasive grains, and beveling the edge of the crystal plate, and etching the whole polished surfaces of the crystal plate, so that the impedance R.sub.1 of the crystal plate is decreased within an allowable range and the Q factor becomes large.
However, the demands of the users for the performance and cost of the crystal resonators have become severe. Therefore, it is now difficult to satisfy the user's demands, even if the manufacturing technique mentioned above is used for manufacturing the crystal resonator. That is to say, the user requires to make the impedance of the crystal resonator much smaller.
Moreover, in the temperature characteristics of the impedance R.sub.1, a non-continued variation, which is so-called dip, is found. This dip is related to a dip of the temperature characteristics of the frequency of the crystal resonator, and thus it is difficult to compensate. Therefore, it is also required by the user that the crystal resonator whose temperature characteristics of the impedance R.sub.1 or frequency has no dip is developed and that the manufacturing cost becomes low.